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Question
Answer the following:
Find `sum_("r" = 1)^"n" "r"("r" - 3)("r" - 2)`
Solution
`sum_("r" = 1)^"n" "r"("r" - 3)("r" - 2)`
= `sum_("r" = 1)^"n" ("r"^3 - 5"r"^2 + 6"r")`
= `sum_("r" = 1)^"n" "r"^3 - 5 sum_("r" = 1)^"n" "r"^2 + 6 sum_("r" = 1)^"n" "r"`
= `("n"^2("n" + 1)^2)/4 - 5("n"("n" + 1)(2"n" + 1))/6 + 6*("n"("n" + 1))/2`
= `("n"("n" + 1))/12[3"n"("n" + 1) - 10(2"n" + 1) + 36]`
= `("n"("n" + 1))/12[3"n"^2 - 17"n" + 26]`
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